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About the book

Description

This consists of the elementary aspects of linear algebra which depend mainly on row operations involving elementary manipulations of matrices. The field of scalars is typically the field of complex numbers.

Content

Preface

Preliminaries

Sets And Set Notation

Functions

The Number Line And Algebra Of The Real Numbers

Ordered fields

The Complex Numbers

Exercises

Completeness of R

Well Ordering And Archimedean Property

Division And Numbers

Systems Of Equations

Exercises

Fn

Algebra in Fn

Exercises

The Inner Product In Fn

What Is Linear Algebra?

Exercises

Matrices And Linear Transformations

Matrices

Exercises

Linear Transformations

Subspaces And Spans

An Application To Matrices

Matrices And Calculus

Exercises

Determinants

Basic Techniques And Properties

Exercises

The Mathematical Theory Of Determinants

The Cayley Hamilton Theorem

Block Multiplication Of Matrices

Exercises

Row Operations

Elementary Matrices

The Rank Of A Matrix

The Row Reduced Echelon Form

Rank And Existence Of Solutions To Linear Systems

Fredholm Alternative

Exercises

Some Factorizations

LU Factorization

Finding An LU Factorization

Solving Linear Systems Using An LU Factorization

The PLU Factorization

Justification For The Multiplier Method

Existence For The PLU Factorization

The QR Factorization

Exercises

Linear Programming

Simple Geometric Considerations

The Simplex Tableau

The Simplex Algorithm

Finding A Basic Feasible Solution

Duality

Exercises

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